Homogenisation theory for Friedrichs systems

Abstract

We develop a general homogenisation procedure for Friedrichs systems.Under reasonable assumptions, the concepts of $G$ and $H$-convergence are introduced.As Friedrichs systems can be used to represent various boundary or initial-boundary value problems for partial differentialequations, some additional assumptions are needed for compactness results.These assumptions are particularly examined for the stationary diffusion equation, the heat equation and a model exampleof a first order equation leading to memory effects.In the first two cases, the equivalence with the original notion of $H$-convergence is proved.